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Given $a = \begin{bmatrix} 1 & 2 & 3 & 4\end{bmatrix}^\top$ and $b = \begin{bmatrix} k_1 & k_2 & k_3 & k_4\end{bmatrix}^\top$, find $\det(I + a b^\top)$.

Rodrigo de Azevedo
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Hikaru
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1 Answers1

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Using Weinstein-Aronszajn,

$$\det \left( {\rm I}_4 + {\rm a} {\rm b}^\top \right) = 1 + {\rm b}^\top {\rm a} = \color{blue}{1 + k_1 + 2 k_2 + 3 k_3 + 4 k_4}$$

Rodrigo de Azevedo
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    thank you very much for editing and answering my question. 本当にありがとうございました – Hikaru Apr 03 '21 at 14:01